f(x) is obtained from x by replacing the last bit with 1 . For example, f(1000-1

Question

f(x) is obtained from x by replacing the last bit with 1 . For example, f(1000-1001 Select the correct description of the function f. a. One-to-one and onto Page 2 of 5 b. One-to-one but not onto c. Onto but not one-to-one d. Neither one-to-one nor onto f(x) is obtained from x by removing the first bit. For example, f(1000) 000 Select the correct description of the function f. a. One-to-one and onto b. One-to-one but not onto c. Onto but not one-to-one d. Neither one-to-one nor onto 12, Q: f: Z Z. f(x) ,x31 Select the correct description of the function f. a. One-to-one and onto b. One-to-one but not onto c. Onto but not one-to-one d. Neither one-to-one nor onto 13, Q: f: Z Z. f(x) = x + 3. Select the correct description of the function f. a. One-to-one and onto b. One-to-one but not onto c. Onto but not one-to-one d. Neither one-to-one nor onto 14.Q:f:Z:Z: f(x) = x + 3. Select the correct description of the function f. a. One-to-one and onto b. One-to-one but not onto c. Onto but not one-to-one d. Neither one-to-one nor onto 4.4 The inverse of a function 15, Q: A = {a, b,c,d) x (1, 2, 3, 4) Each choice defines a function whose domain is A and whose target is X. Select the function that has a well-defined inverse a-f= {(a, 3), (b, 4), (c, 3), (d, 4)} b-f= {(a, 3), (b, 3), (c, 3), (d, 3)} c. f = {(a, 3), (b, 4), (c, 2), (d, 1)} d-f= {(a, 3), (b, 4), (c, 2), (d, 4)}

Explanation / Answer

10.

f is not one-to-one because there are multiple x mapped to the same f(x)

e.g. f(1000) = 1001

f(1001) = 1001

f(1002) = 1001

f is not onto, because all elements of codomain can be obtained from output of f(x)

e.g. 1002 can never be obtained.

so answer is (d)

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